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MPRAMunich Personal RePEc Archive
”But Can’t we Get the Same Thing witha Standard Model?” RationalizingBounded-Rationality Models
Spiegler, Ran
University College London, Tel Aviv University
15. March 2010
Online at http://mpra.ub.uni-muenchen.de/21428/
MPRA Paper No. 21428, posted 15. March 2010 / 23:01
“But Can’t we Get the Same Thing with a
Standard Model?”
Rationalizing Bounded-Rationality Models∗
Ran Spiegler†
March 15, 2010
Abstract
This paper discusses a common criticism of economic models that depart from
the standard rational-choice paradigm - namely, that the phenomena addressed
by such models can be “rationalized” by some standard model. I criticize this
criterion for evaluating bounded-rationality models. Using a market model with
boundedly rational consumers due to Spiegler (2006a) as a test case, I show
that even when it initially appears that a bounded-rationality model can be
rationalized by a standard model, the rationalizing models tend to come with
unwarranted “extra baggage”. I conclude that we should impose a greater burden
of proof on rationalizations that are offered in refutation of such models.
∗I thank Ayala Arad, Yves Guéron, Barton Lipman, Ariel Rubinstein and participants at theSummer School in Economics and Philosophy, San Sebastian 2009, for their comments. Financialsupport from the European Research Council, Grant no. 230251, as well as the ESRC (UK), isgratefully acknowledged.
†Tel Aviv University and University College London. E-mail: [email protected]. URL:http://www.homepages.ucl.ac.uk/~uctprsp
1
- I am not the Messiah, would you please listen, I am not the Messiah, do
you understand? Honestly!
- Only the true Messiah denies his divinity.
- What? Well, what sort of chance does that give me? All right! I am the
Messiah!
- He is! He is the Messiah!
(Monty Python’s Life of Brian)
1 Introduction
One side effect of the growing popularity and influence of behavioral economics has been
the profusion of discussions of the methodology and rhetoric of economic theory (see
Caplin and Schotter (2008) for a representative collection of essays, as well as Rabin
(2002), Rubinstein (2006), Bernheim (2009), Dekel and Lipman (2009), Binmore and
Shaked (2010)). This paper aims to add a dimension to this debate.
To motivate the discussion, think of the following familiar situation. You are sitting
in the audience of an economic theory seminar. The speaker is presenting a model of
a certain economic phenomenon, in which some of the economic agents are boundedly
rational in some way. As the speaker is going through her model, you are beginning
to sense that although this may be an interesting exercise, the model could be entirely
recast in terms of a standard model with rational agents, possibly with an added
conventional source of friction such as imperfect information or search costs. You are
preparing to raise your hand...
This paper is about what happens next - or, to be more precise, about what should
happen next. How should we conduct our debates about explanations of economic
behavior that are based on non-standard behavioral assumptions? In particular, how
should we compare these explanations with more conventional explanations based on
rational choice? Should we devalue a bounded-rationality model (BRM henceforth)
when it the economic phenomenon it addresses seem to be explicable by a rational-
choice model?
As the above not-so-imaginary scenario suggests, these questions are not motivated
by abstract philosophizing, but on my own direct experience on both sides of the fence,
both as a member of seminar audiences and as a theorist who has been preoccupied
with economic models in which at least some agents are boundedly rational. From
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this experience (as well as others’ - see Rabin (2002)), a major share of the comments
contributed by referees and seminar audiences in response to a BRM can be read as
attempts to “rationalize” the model. As an inventor of bounded-rationality models, I
often feel an internal need to compare such models with more conventional ones based
on rational choice. And when I do not feel this need myself, I can always count on
seminar audiences, referees and coffee-machine conversation partners to fill the gap.
The audience’s basic criticism can be summarized as follows:
Although BRMs may shed some light on economic phenomena, in many
cases one could think of a rational-choice model that could account for
these phenomena. And if we can “get the same thing” with a standard
model, why should we depart from the rational-choice paradigm? Moreover,
since rational-choice models and BRMs tend to have dramatically different
welfare implications, a switch from rational-choice to BRMs is not only
problematic methodologically, but also carries a significant cost in terms of
its implied policy prescriptions.
This paper is an attempt to come to terms with this “can’t we get the same thing with
a standard model?” critique. The methodological problem at hand is fundamentally
theory selection: how should we choose from a number of competing models that
provide different explanations for a given phenomenon? The need to choose is only
magnified by the models’ diverging welfare implications. The normatively scientific
way of making this choice is to tease out cases in which the models generate different
predictions, and subject these predictions to an empirical test. However, economics
being the dismal science that it is, such empirical tests are difficult and rare. Indeed,
the whole point of the “can’t we get the same thing with a standard model” critique
is that since the two types of explanations are empirically hard to distinguish, the
conventional rational-choice explanation should be given priority.
Therefore, for the purpose of our discussion here, I will set aside the question of
empirical tests and take it for granted that the account a BRM in question provides
for certain economic phenomena is sound: the “story” it tells “rings true”; its behav-
ioral assumptions seem to fit generally known psychological principles and the market
situation in question; and its predictions are broadly consistent with known (stylized)
facts. What the “can’t we get the same thing with a standard model” critique main-
tains is that for the purpose of making these predictions, one does not have to abandon
conventional behavioral assumptions, and therefore one ought not to; even if there is
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some truth in the bounded-rationality story, the same truth could be captured equally
well by a rational-choice model. I refer to such a rational-choice model that is offered
in refutation of a BRM as a “rationalization”, or as a “rationalizing model”.
My discussion so far may have given the impression that every BRM faces a sin-
gle, well-defined rationalization. This is obviously not the case. The rational-choice
paradigm is famously flexible, and there is a variety of conventional models that can
be offered in refutation of any given bounded-rationality model. Rationalizing models
tend to come in one of the following three forms:
Rationalization via modified information. The rationalizing model modifies the bounded-
rationality model by replacing the boundedly rational agents with conventionally ra-
tional agents who happen to have different information.
Rationalization via modified preferences. The rationalizing model modifies the bounded-
rationality model by replacing the boundedly rational agents with conventionally ra-
tional agents who happen to have different preferences.
Rationalization via endogenization. The rationalizing model refuses to take the behav-
ioral rule assumed by the bounded-rationality model as truly exogenous,and instead
derives it as a rational equilibrium response in a larger model that introduces frictions
which are not explicitly included in the original model.
I could illustrate these forms with any number of BRMs from the literature. For
expositional effectiveness, however, I adopt a case study approach and restrict atten-
tion to a single model, due to Spiegler (2006a), of price competition in markets for
credence goods when profit-maximizing firms face consumers who use naive anecdotal
reasoning to evaluate stochastic variables. This model was proposed to highlight as-
pects of industries such as alternative medicine, consulting and mutual funds. There
are several reasons for this expositional strategy, apart from my obvious familiarity
with the model in question. First, a case study approach is useful because fine details
turn out to matter. Second, the model in question is extremely simple to begin with.
This facilitates the formulation of explicit rationalizing models and enables an intelli-
gible comparison with the original model. Were the BRM itself more complex to begin
with, detailed comparison with its rationalizations would quickly become intractable.
The rationalizing models that are offered in refutation of Spiegler (2006a) are
themselves based on ideas made by flesh-and-blood seminar audiences, referees and
colleagues in corridor conversations. I hope that I have done full justice to these sug-
gestions. The sparseness of the original model makes it a particularly easy target for
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the “can’t we get the same thing with a Standard Model?” critique, because it is easy
to think of conventional frictions that are excluded from the original model. Never-
theless, I show that even in this ideal case, the “can’t we get the same thing with a
standard model” criticism is plagued with several difficulties, which can be summarized
as follows:
• The rationalizing model changes not only assumptions regarding individual be-havior, but also assumptions regarding the external environment that individuals
face.
• The rationalizing model introduces new parameters into the model. Replicationof the original BRM’s predictions hinges on proper selection of parameter values.
• The rationalizing model may give rise to multiple equilibria, whereas the originalBRM has a unique equilibrium. Replication of the BRM’s predictions hinges on
proper selection of equilibrium.
• Changed assumptions about individual behavior mandated by the rationalizingmodel may be implausible in the context of the applications of the original BRM.
• Natural extensions of the original BRM can be meaningless under the rational-
izing model.
These are essentially problems of how to assign burden of proof in a debate: which
desiderata should the rationalizing model satisfy in order to count as a successful refuta-
tion of the BRM? For instance, when the rationalization introduces new unobservable
parameters and replicates the original BRM’s predictions under a suitable selection
of parameter values, does this diminish its power as a “devastating criticism” of the
BRM? In the concluding section, I offer my own opinion about how we should regard
“rational explanations” that are offered as a criticism of BRMs. But my main objective
in this paper is simply to expose the burden-of-proof problems themselves, because I
believe that heightened awareness of these problems could improve the quality of our
debates over BRMs.
I should to make three caveats:
• We need to distinguish the program of rationalizing models of economic behaviorthat depart from the rational-choice paradigm from the time-honored tradition of
rationalizing observed economic behavior that superficially contradicts rational
choice. This paper is entirely about the former.
5
• My discomfort with the “can’t we get the same thing with a Standard Model?”critique of BRMs does not imply a rejection of other criticisms of BRM: their
scope tends to be limited in comparison with the impressive generality of the
basic rational-choice models; they are perceived as arbitrary and post-hoc relative
to their rational-choice counterparts; and they violate the cherished revealed
preference principle. These concerns are often justified but have been debated
elsewhere, whereas the “can’t we get the same thing with a Standard Model?”
critique has not been subjected to careful methodological scrutiny.
• I refrain from considering rationalizations that restore the rationality of an agent’sbehavior by describing it as an optimal response to an incorrect subjective model.
The reason is simple: I do not view such rationalizations as being standard at all.
Conventional economic models invariably assume a common understanding of the
model, such that any asymmetry in the agents’ beliefs is fully embedded in the
model itself. The only subjectivity that standard models admit is non-common
priors. (However, violating the common-priors assumption would probably be
deemed “non-standard” twenty years ago.)
The remainder of the paper is structured as follows. Section 2 presents the simplest
version of the model due to Spiegler (2006a). Sections 3-5 subject this model to the
three forms of the “can’t we get the same thing with a Standard Model?” critique. I
discuss my lessons from these rationalization exercises in Section 6.
2 A Market Model with Boundedly Rational Con-
sumers
Imagine a market that consists of a continuum of identical consumers and n identical
firms. Consumers enter the market with some problem. The value of fixing it is 1 for
all consumers. Each firm i sells at zero cost a product that fixes the problem with
independent probability α ∈ (0, 1). Consumers also have an outside option (“doingnothing”), labeled i = 0, which fixes their problem with the same probability α. Firms
are standard profit maximizers. They compete by choosing prices simultaneously. Let
pi ∈ [0, 1] denote the price chosen by firm i. Assume that p0 = 0 - that is, “doing
nothing” costs nothing.
I will refer to the firms as “quacks”, as they display no skills relative to “doing
nothing”. There are several real-life situations that seem to fit this specification. Ac-
6
tively managed mutual funds are a case in point. According to the Efficient Market
Hypothesis, prices in financial markets fully reveal private information. Consequently,
an actively managed mutual fund cannot generate (risk-adjusted) returns in excess of
the market portfolio. Thus, under the Efficient Market Hypothesis, the market for
actively managed mutual funds is a “market for quacks”. And of course, as the term
“quacks” indicates, practitioners of non-scientific medicine often fall into this category.
If consumers chose rationally with respect to a correct understanding of the above
market model, the market for quacks would be inactive, as all consumers would choose
the outside option.1 I refer to this outcome as the rational-consumer benchmark. In-
stead, let us assume that consumers choose according to the following procedure. Each
consumer independently draws one sample point from each alternative (including the
outside option). For every i = 0, 1, ..., n, let xi denote the outcome of the consumer’s
sampling of alternative i: xi = 1 (the problem is fixed) with probability α and xi = 0
(the problem is not fixed) with probability 1−α. Given a sample, the consumer choosesan alternative i that maximizes xi − pi. (Let us ignore the case of ties.) The outcome
of the consumer’s choice i is a new, independent draw; therefore, his expected payoff
is α− pi.
The consumers’ choice procedure induces a complete-information, simultaneous-
move game played by the firms. To illustrate the firms’ payoff function, suppose that
pn > pn−1 > · · · > p1 > p0 = 0. Then, firm k’s expected payoff is
p · α · (1− α)k
The reason is that the firm’s clientele consists of all consumers who obtained a good
sample point about the firm’s product and a bad sample point about all of cheaper
alternative. Thus, if all firms play a mixed strategy given by a continuous cdf G, then
the expected payoff that a price p in the support of G generates for an individual firm
is
p · α · (1− α) · [α(1−G(p)) + (1− α)]n−1
The max-min payoff in this game is α(1− α)n.
This game has a unique Nash equilibrium. The equilibrium is symmetric: each firm
plays a mixed strategy given by the following cdf :
G(p) =1
α− 1− α
α· p−1/(n−1)
1There are also Nash equilibria in which a non-empty subset of firms set p = 0 and consumerschoose these firms.
7
defined over the support [(1−α)n−1, 1]. Each firm earns its max-min payoff in equilib-
rium, hence equilibrium industry profits are
nα(1− α)n
The equilibrium has several noteworthy features:
Consumer behavior. The market for quacks is active and consumers pay positive prices
for what is ultimately a useless product. Moreover, there is a positive clientele for each
firm, including the most expensive one. Given a realization of the strategy profile, the
size of the clientele of the firm that charges the kth-lowest price is α · (1− α)k.
Comparative statics: prices. Expected price goes up as α goes down, and converges
to the monopoly level p = 1 as α tends to zero. The reason is that as α gets closer
to zero, the probability of multiple successes in the consumer’s sample goes down, and
therefore each firm is effectively unlikely to face competition.
Comparative statics: industry profits. Industry profits are hump-shaped with respect
to the number of competitors n. The intuition for this effect is straightforward. On one
hand, a greater number of firms increases the incentive to cut prices. This is a standard
“competitive” effect. On the other hand, a greater number of market alternatives
increases demand for the industry as a whole, because there is a higher chance of
hearing a good anecdote about some product. This is an “exploitative” effect. Fixing
α, the exploitative effect outweighs the competitive effect when n is relatively small
(the critical value of n for which this is overturned increases as α decreases). Note that
industry profits are a pure transfer from consumers to firms, given our assumption that
the probability that the consumer’s problem gets fixed is independent of his decision.
Thus, all the statements regarding industry profits are at the same time statements
about consumer welfare.
Having presented the basic BRM, let us turn to its rationalizations.
3 Rationalization via Modified Information
Replacing imperfect rationality with imperfect information is perhaps the most im-
mediate and common of traditional responses to models of bounded rationality. The
idea is to replace what seems like a decision error resulting from bounded rationality
with a rational response to limited information. For instance, choosing a low-quality
product over an identically priced, high-quality product can be interpreted as evidence
8
of imperfect information regarding product characteristics.
In the case of the market-for-quacks model, this rationalization is very naturally
suggested by the sampling-based procedure itself. Instead of viewing the samples as
part of the choice procedure in a complete-information model, we can re-interpret the
samples as information sets in a model in which consumers are imperfectly informed.
The rationalization turns the model into an incomplete-information extensive-form
game: firms move first (making simultaneous pricing decisions) and consumers move
second, after receiving partially informative signals of the firms’ success rates. This
model’s predictions are given by applying the solution concept of sequential equilibrium
to the incomplete-information game. In the BRM, consumers confront their market
environment with a decision procedure that generates systematic inference errors. In
contrast, the imperfect-information rationalizing model rules out systematic inference
errors because the solution concept of sequential equilibrium embodies “rational ex-
pectations”.
This rationalization sounds highly plausible. As we shall see, it gives rise to symmet-
ric Nash equilibria in which firms play mixed pricing strategies and a positive fraction
of consumers choose firms over the outside option. Nevertheless, the rationalization
suffers from a number of difficulties.
Changed assumptions about the external environment
In order for consumers’ imperfect information to have any relevance, we must assume
that firms have multiple payoff-relevant types - e.g., a high-quality firm and a low-
quality firm. Thus, in order to apply the rationalization, we also need to modify our
assumptions about the external market environment.
This is not an innocuous modification. For example, consider the market for home-
opaths. A homeopathic medicine is based on a solution so diluted that it is, to an
excellent approximation, pure water. To claim that there are high-quality and low-
quality homeopaths is to claim that different types of water have different therapeutic
properties.2
In another context, if we consider the money-management application of the model,
the assumption that there are high-quality and low-quality money managers means that
some managers can systematically beat the market. This is an important substantive
assumption, which is not taken lightly by financial economists. One should continue
not to take it lightly when using it to rationalize models of money management markets
2Alternatively, a higher-quality homeopath could be regarded as one who is better at generating aPlacebo effect. However, admitting Placebo effects reintroduces irrationality through the back door,and therefore I ignore this possibility.
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with boundedly rational investors.
New unobservable parameters
The incomplete-information game designed to rationalize the market-for-quacks model
requires us to introduce new parameters that describe the distribution of firm types
and the consumers’ signal structure. The following specification is minimalistic in
this regard. Each market alternative (the firms as well as the outside option) has
a type t ∈ {L,H}. The prior probability of L is λ, independently across market
alternatives. When a consumer chooses an alternative of type t, his need is satisfied
with probability αt, where 1 ≥ αH > αL > 0. Thus, each alternative’s ex-ante success
rate is α = λαL+(1−λ)αH . Each consumer observes a signal si ∈ {L,H} about eachalternative. The signals are distributed independently across market alternatives and
across consumers. Let qts denote the probability that the consumer observes the signal
s conditional on the alternative’s type being t. Assume that qLL > qLH and qHH > qHL
- i.e., signals have some informational content.
Notice how many new parameters have been introduced, even in such a minimalistic
two-type, two-signal rationalization: αL, αH , qLL, qLH , qHL, qHH (λ is not an indepen-
dent parameter, as it is determined by αL, αH and α.) In contrast, the market-for-
quacks model essentially had a single parameter, namely the firms’ ex-ante success rate
α. Also, note that if αH = αL, consumers know with certainty that they are in a mar-
ket for quacks, and the model collapses to what I referred to as the rational-consumer
benchmark. Therefore, in what follows we must insist that αH > αL.
Does the rationalizing model replicate the original model’s key predictions?
Let us explore sequential equilibria in this incomplete-information game, and com-
pare them to the unique Nash equilibrium in the market-for-quacks model. Formal
near-equivalence between the original model and its rationalization is attained for the
following parameter values: αH = 1, αL = 0, and qHH = qLL = 1. That is, high-quality
(low-quality) alternatives satisfy the consumer’s need with probability one (zero), and
the consumer is perfectly informed of the alternative’s type. The equilibrium strategy
for high type firms is the same as in the basic model. Low types are always recognized
as such and are never chosen, and so their pricing strategy is indeterminate as well as
irrelevant for the market outcome.
The reason I refer to this as “near-equivalence” is two-fold. First, we should have
compared the firms’ ex-ante pricing strategy in the rationalizing model to the equilib-
rium strategy in the original market-for-quacks model. Instead, we compared the latter
to the equilibrium behavior of high-quality firms in the rationalizing model. Second,
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and more importantly, the two models generate different consumer behavior. In the
rationalizing model, all consumers make the same decision in equilibrium. They are all
informed of the firms’ types, and since firms play continuous pricing strategies, price
ties occur with probability zero. Therefore, all consumers make the same choice: they
select the cheapest high-quality alternative (or the outside option, if no high-quality al-
ternative is available). In contrast, recall that a salient feature of the market-for-quacks
model was that each firm - including the most expensive one - had a positive clientele.
Here, the most expensive firm ends up with either no clients or with all clients. In light
of this discrepancy in the predictions that these two models make regarding consumer
behavior, should we view this rationalization as successful?
The parameter values in this specification of the rationalizing model are also prob-
lematic in terms of interpretation. They imply that consumers are perfectly informed
of the types of all market alternatives, while firms receive no signal about their oppo-
nents’ types. It is not easy to think of market situations for which this would be a
plausible assumption. And in any case, recall that our motivation was to replace im-
perfect rationality with imperfect information about firms’ types, yet consumers turn
out to be perfectly informed under these parameter values.
When we turn to more plausible parameter specifications, the rationalizing model
fails to reproduce salient features of firm behavior in the original model. Recall that in
the market-for-quacks model, the firms’ equilibrium pricing strategy is a continuously
increasing cdf over the interval [(1− α)n−1, 1]. That is, firms charge prices that range
all the way up to consumers’ willingness to pay for guaranteed satisfaction of their
need, and these prices generate a positive clientele. Can sequential equilibrium in the
rationalizing model reproduce this effect?
When consumers are imperfectly informed of the firms’ types, the firms’ pricing
strategy in equilibrium is independent of their type, because there is nothing in the
incentive structure in the model that enables firms to signal their type. In other
words, equilibrium must be pooling. (Note, however, that in other cases, rationalization
via modified information does introduce signalling issues that give rise to multiple
equilibria. In this case, the rationalizing model’s ability to replicate the predictions
of the target bounded-rationality model relies on suitable equilibrium selection, thus
raising a burden-of-proof problem similar to the parameter selection problem discussed
here.)
By Bayes’ rule:
Pr(t = H | s = H) =λqHH
λqHH + (1− λ)qLH
11
Therefore, when a consumer observes a good signal about an alternative, the alterna-
tive’s posterior success rate is
α | H =λqHHαH + (1− λ)qLHαL
λqHH + (1− λ)qLH
Similarly, when a consumer observes a bad signal about an alternative, the alternative’s
posterior success rate is
α | L = λqHLαH + (1− λ)qLLαL
λqHL + (1− λ)qLL
In order for a consumer to be willing to pay a positive price for a firm, it must
be the case that he received a bad signal about the outside option. This is just as in
the market-for-quacks model. The reason is that all market alternatives are symmetric
in terms of ex-ante quality, but the outside option comes free whereas firms charge
positive prices. Therefore, the maximal price that consumers are willing to pay to
firms is (α | H) − (α | L). This has to be the maximal price in the support of themarginal equilibrium pricing strategy. It is easy to see that (α | H) − (α | L) ≤ 1.This inequality is strict unless qHH = αH = 1 and qHL = αL = 0, which is the case we
already covered above. Thus, the price range cannot be replicated under reasonable
assumptions on the signal structure.
It could be argued that the range of equilibrium prices is not a key prediction of
the original model, because of the difficulty of observing the consumers’ underlying
willingness to pay. But the rationalizing model also fails to reproduce the market-for-
quacks model’s comparative statics. As αL and αH go down, it is easy to see that
since qLL > qLH and qHH > qLH , (α | H) − (α | L) decreases as well. Therefore, themaximal price that consumers are willing to pay in the rationalizing model goes down.
In the limit, as αL and αH tend to zero, the maximal price converges to zero. This is
in marked contrast to the effect of lowering ex-ante success rates on equilibrium prices
in the original market-for-quacks model.3
To summarize, in the zoo of new parameters that are needed to specify the ratio-
nalizing model, there is a configuration of parameter values that roughly replicates the
firms’ equilibrium behavior in the market-for-quacks model. However, this configura-
tion is inconsistent with the motivation of imperfect informed consumers. Indeed, it
has a difficult-to-interpret property that consumers are fully informed of firms’ quality,
3There are other ways to manipulate the rationalizing model’s parameters in a way that lowers theex-ante success rate. For instance, we can reduce λ without changing αL or αH . This would have asimilar effect.
12
while firms do not receive any signal about their opponents’ quality. Furthermore,
consumer behavior in equilibrium differs from the market-for-quacks model. For all
other configurations of parameter values, the rationalizing model fails to replicate the
original model’s range of equilibrium prices, and the comparative statics of expected
prices with respect to the ex-ante success rate are diametrically opposed to what the
original model predicts.
Summary
Our analysis has raised several questions regarding the burden of proof we may wish to
impose on the rationalizing model. How should we evaluate a rationalization when it
requires us to modify assumptions about the external environment, particularly when
these are essential to the “moral” of the original story? Should we discount the ratio-
nalizing model if it forces us to introduce a number of new parameters? Is it enough to
replicate the firms’ behavior, or do we need to reproduce consumer behavior as well,
in order for the rationalization to count as a success? Is it enough to find particular
parameter values that replicate certain aspects of the original model’s equilibrium? Or
should the replication hold for a large range of parameter values? What is the inter-
pretational burden on the parameter values that are used for replicating the original
model’s predictions?
4 Rationalization via Modified Preferences
When a certain choice pattern appears like a decision error that results from bounded
rationality, we should entertain the possibility that what seems like an error is in fact a
perfectly rational decision, and the only reason it seems erroneous is that we, as outside
observers, attribute the wrong preferences to the agent. For instance, a manager’s
failure to choose a profit-maximizing project can be interpreted as evidence of a career
concern. Replacing a behavioral model based on boundedly rational reasoning with a
rational-choice model in which the consumer’s preferences are re-specified is another
common form of rationalizing BRMs.
Unlike the rationalization via modified information, rationalization via modified
preferences turns out to be extremely effective in the case of the market-for-quacks
model. Drop the assumption that consumers are interested in the firms’ products
only because they expect it to fix their problem. Instead, assume that there is an
idiosyncratic value for each consumer-firm match. Specifically, a consumer’s evaluation
of each alternative i ∈ {0, 1, ..., n} is ui − pi, where ui gets the values 1 or 0, with
13
probabilities α and 1− α, independently across alternatives and consumers.
Rational consumers with this specification of independent private values behave
exactly like boundedly rational consumers who evaluate alternatives according to the
sampling procedure. Therefore, the rationalizing model is formally - and therefore
behaviorally - equivalent to the market-for-quacks model. This is an extreme case of the
methodological dilemma which motivated this paper. The formal equivalence between
the two models means that every prediction about market outcomes that we make in
one model is perfectly mimicked by the other. However, the welfare implications are
radically different. The BRM implies that in a “market for quacks” (where the success
rate of any product traded in the market is no different from the outside option of
doing nothing), industry profits are a pure welfare loss for consumers. This loss can
grow with the number of competitors. In contrast, in the rationalization, the market
serves genuine consumer needs. It is welfare enhancing, and a greater number of firms
is unambiguously better for consumers because it gives consumers access to a greater
set of alternatives to choose from, while lowering their prices.
How should we compare these two accounts?
Prior plausibility of behavioral assumptions
I do not see any escape from the need to judge the prior plausibility of the behavioral
assumptions that underlie two, formally equivalent models, in the context of their
intended application. For instance, when the market in question is for forecasting
services, then assuming independent private values makes little sense: every rational
consumer should prefer a forecaster who makes more accurate predictions. In contrast,
when the market in question is for self-help guides, both explanations are plausible.
On one hand, independent private values make sense because different self-help guides
may contain different pieces of advice that fit different people. On the other hand,
casual observation suggests that people extrapolate naively from anecdotal evidence to
evaluate self-help guides.
The only reason that I mention this obvious point is that there is a strong tradi-
tion in economic methodology (following Friedman (1953)) that is opposed to a priori
judgments of behavioral assumptions and preaches that we evaluate models exclusively
by their predictive success. However, when we need to choose between two formally
equivalent models having different welfare implications, Friedman’s positivistic crite-
rion is too weak, and it seems clear to me that we should favor the model that is based
on behavioral assumptions that make better sense in the relevant context.
Extended models
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Even when two different models appear equivalent, they may differ when we move out-
side the original environment for which they were formulated. That is because different
models tend to suggest different extensions. For example, Spiegler (2006b) extends the
model of market competition with consumers who follow the sampling procedure, by
allowing firms to randomize over prices. The extension presupposes that the same
element of bounded rationality that made consumers extrapolate naively from small
samples when evaluating the random performance of credence goods is going to make
them extrapolate naively from small samples to evaluate random pricing strategies.
Spiegler (2006b) shows that this behavioral model implies a strict incentive for firms to
randomize over prices. Moreover, a greater number of competitors results in a mean-
preserving spread in the equilibrium price distribution that firms adopt. In contrast, it
is hard to think of an organic extension of the differentiated-taste rationalization of the
market-for-quacks model that will generate these effects. Should the observation that
the BRM and its rationalization become behaviorally distinct in an enlarged domain
affect our judgment of the rationalizing model in the original domain?
Although the idea that extensions can break formal equivalence between two models
is familiar, it has certain subtleties. Consider another extension of the market-for-
quacks model, discussed in Spiegler (2006a), in which firms choose not only prices but
also (simultaneously) whether to disclose their success rates to consumers. Disclosure
is meaningless under the differentiated-taste rationalization, because its premise is
that consumers are better informed than firms, and not the other way around. One
could argue that this by itself provides a meaningful distinction between the sampling-
based model and its differentiated-taste rationalization. However, it turns out that the
equilibrium prediction of the extended model is that firms choose not to disclose their
success rates. Therefore, as far as equilibrium behavior is concerned, the two models
are equivalent after all. In the sampling-based model, disclosure is meaningful but fails
to occur in equilibrium, while in the differentiated-taste rationalization, disclosure does
not occur because it is meaningless in the first place. Can we legitimately say that the
differentiated-taste rationalization replicates the sampling-based model’s predictions in
the extended domain that includes disclosure?
Summary
In this section we examined a rationalization that looks perfect at first glance, as
it is formally equivalent to the original BRM. However, we identified two burden-of-
proof issues. First, the behavioral assumptions underlying the rationalizing model may
be implausible in the context of the original model’s intended domain applications.
Second, determining the relevant domain itself is not straightforward, because the
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original model has natural extensions that are either nonsensical from the point of
view of the rationalizing model, or generate predictions which are distinct from those
of an analogous similar extension of the rationalizing model. How should we evaluate
the rationalizing model in light of these observations?
5 Rationalization via Endogenization
Another way of rationalizing a BRM is to argue that the behavior it generates appears
to be non-rational only because the model leaves out certain costs associated with the
decision process. Once these are explicitly incorporated into the model, rationality is
restored. In the extended model, the consumer chooses how much mental resources to
spend on the decision problem, on the basis of “rational expectations” of the benefits of
information processing. Note that it is not so much the friction as its formal treatment
that is conventional. Decision costs are rarely incorporated into standard economic
models. However, the type of extended model described above is conventional in that
it treats decision costs as if they were search costs, or costs of acquiring information.
The following example has become almost canonical in methodological discussions
of BRMs. (see Caplin and Schotter (2008)). An American tourist visits London (the
tourist is invariably American in tellings of this story). Before crossing a street, he looks
left, sees that the road is clear, starts walking, and gets hit by a car coming from his
right. The bounded-rationality interpretation of the tourist’s behavior is that he does
not deliberate over his decision problem (when to cross the street). Instead, he follows
an automatic rule that may be optimal in his home environment. A rationalization
that incorporates information-processing costs would proceed as follows. The tourist
realizes that he is on foreign soil and that he needs some time to remember which side
the cars are coming from. However, spending time on this mental task is costly. The
tourist rationally trades off this cost against the benefit of safe crossing.
As this example is only meant to illustrate a methodological dilemma, I will not
get into a detailed discussion of the plausibility of the rationalization of the tourist’s
behavior. I will only comment that the two explanations of the tourist’s behavior are in
principle distinguishable. For instance, one could put up a sign for pedestrians saying
“don’t cross the street without thinking first”. This intervention would have an impact
only under the bounded-rationality interpretation.
Let us turn back to the market-for-quacks model. The consumer’s procedure of
sampling each market alternative and selecting the best alternative in the sample can
be viewed as an optimal strategy in a larger model, in which we introduce search costs.
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In such an extended model, there is an arbitrarily large number of firms. The consumer
optimally designs a sample, taking into account the cost of obtaining information about
the firms’ quality and pricing decision. In this way we endogenize n as the size of the
consumers’ sample, given their correct expectation of the firms’ equilibrium pricing
strategy.
This rationalization shares all the problems of the rationalization method discussed
in Section 3. In particular, the equilibrium pricing strategy can be replicated only if
we assume that when a consumer samples a firm, he obtains perfect information about
its type (whereas the firm’s opponents are uninformed). We have already commented
on the implausibility of this informational assumption. At any rate, in this case, it is
easy to come up with a cost of obtaining a single sample point, for which the number of
firms that the consumer samples will be optimal ex-ante, given their pricing strategy.
However, the assumption that the consumer commits ex-ante to the size of his sample
is problematic. Suppose that the consumer has sampled n firms, and all of them - as
well as the outside option - turned out to be of low quality. As the cost of obtaining
these sample points is sunk, what prevents the consumer from obtaining new sample
points?
Rationalization via endogenization is an interesting modelling exercise. However,
as a criticism of a BRM, it suffers from several methodological difficulties.
When should we endogenize informational constraints?
Any informational constraint in any economic model could be endogenized, by enabling
agents to invest resources that help them relax their constraint. Economists address
this endogeneity only when they wish to focus on the information acquisition process,
and in most applications they are happy to treat the informational limitations as
exogenous, because this is a good modeling strategy. The same standard should hold
for rationality constraints. If the modeler has good reasons for certain restrictions on
the process by which the consumer receives word-of-mouth information in the form of
anecdotes, and a much fuzzier notion of the restrictions that could be imposed on the
costs of actively looking for such anecdotes, then it is a good modelling strategy to
take the sampling procedure as primitive.
At which scale should we endogenize informational constraints?
Even if the sampling procedure is a result of some optimizing process that takes into
account information-processing costs, the optimization often takes place not on a case-
by-case basis, but at a “general equilibrium” level, or on an “evolutionary” time scale.
Consumers devise heuristics and calculational short-cuts that are meant to work well
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on average across a large number of market (as well as non-market) situations. The
sampling procedure is such a calculational short-cut. For the kind of partial equilib-
rium analysis that economists apply in Industrial organization, taking the consumer’s
decision rule as given is a good approximation.
A “Lucas critique”
In order for rationalization via endogenization to be operational, the consumer’s opti-
mization must be made on the basis of correct knowledge of the market equilibrium.
Otherwise, we are not dealing with a rationalization, but merely shifting the element
of bounded rationality to another level. The rational-expectations restriction often
restricts the class of behavioral parameters of the original model which can be derived.
For example, in the case of the market for quacks, we could imagine that certain pairs
of parameter values (α, n) are simply inconsistent with equilibrium under the rational-
izing model. In contrast, the market-for-quacks model does not impose any constraint
on the range of values that they can get.
One point of view is that such a failure to rationalize certain specifications of the
BRM should be regarded as a criticism of the BRM, akin to the famous Lucas cri-
tique of traditional Keynesian macroeconomic models (Lucas (1976)). According to
this interpretation, the fact that certain specifications cannot be justified as equilib-
rium responses in a larger model that incorporates explicit information-processing costs
means that these specifications are illegitimate. Note the rhetorical cunning at play
here. So far, we have viewed success at rationalizing bounded-rationality models as a
vindication of the “can’t we get the same thing with a standard model” critique. Now,
the “Lucas critique” turns the rationalization program on its head, and sees its failure
as a reason to detract the bounded-rationality model. Nothing better illustrates the
trickiness of debates over bounded-rationality models.
6 Discussion
This paper has been concerned with the following dilemma: what is the burden of proof
that should be imposed on a rational-choice model (referred to as RM in the sequel)
that is offered in refutation of a given BRM? The following scenarios abstract from the
details of the specific case study we examined. Each scenario raises a difficulty in the
evaluation of RM as a successful rationalization/refutation of BRM.
• RM mimics key predictions of BRM, but RM differs from BRM not only in
behavioral assumptions, but also in assumptions about the external environment.
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• RM introduces new parameters that were not included in BRM. Whether RM
mimics key predictions of BRM depends on a suitable selection of parameter
values.
• BRM and RM are observationally equivalent in a certain domain, but BR is based
on behavioral assumptions that appear more plausible in this particular domain.
• BRM and RM are observationally equivalent in a certain domain of market situ-
ations, but become distinct when we extend (in a “natural” way) the behavioral
models underlying BRM and RM to a broader domain.
• BRM and RM are observationally distinct out of equilibrium, but they imply
identical equilibrium behavior. An extreme case is where a certain action is
meaningful in BRM yet not taken in equilibrium, while the same action is mean-
ingless and inconceivable a priori in RM.
• RM has multiple equilibria whereas BRM has a unique equilibrium. Whether
RM mimics the predictions of BRM depends on a suitable equilibrium selection.
These difficulties should make us wary of the “can’t we get the same thing with a
standard model” critique. In my opinion, we should subject “rational explanations”
are offered in refutation of BRMs to stricter burden-of-proof requirements. At the very
least, the criteria that we use to evaluate rationalizing models should not differ from
those that we use to evaluate two rational-choice explanations. If a certain prediction
of a given model is qualified by a particular choice of parameter values or a particular
assumption about the external environment, we should not discard these qualifications
simply because the model is offered in refutation of a BRM.
We should also be reluctant to tamper with assumptions of a bounded-rationality
model that concern the domain of market situations that agents face. Whether a
model is static or dynamic, whether its informational constraints are endogenous or
exogenous, whether agents are assumed to be homogenous or heterogeneous - these
are all modeling choices that the theorist makes to define the limits of the theoretical
exercise he wishes to pursue. We are not forced to respect these assumptions when
discussing the model’s merits and drawbacks, but we should try to accept them as
given when advancing alternative “rational explanations”.
If the “can’t we get the same thing with a standard model” critique is so problem-
atic, why is it so popular? I believe that the reason is simple: are we used to looking
for “rational explanations”. It is what we do for a living. Rationalizing behavior is
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an important part of what defines economic theory, and it has had great successes.
Rationalizations of superficially non-rational behavior continue to the subject of very
interesting works (e.g., Samuelson (2001), Compte and Postelwaite (2005), Kamenica
(2008), Baliga and Ely (2009)). The “can’t we get the same thing with a standard
model” critique simply extends this type of reasoning. We are so effortless in our
search for rational explanations that we tend to overlook the rough edges, especially
when we have a prior inclination to reject explanations of economic behavior that de-
part from the rational-choice paradigm. But I hope that this paper has shown that a
modeling style can be very useful for understanding phenomena, and yet quite weak
as a way of criticizing models that follow alternative modeling styles.
References
[1] Baliga, S. and J. Ely (2009), “Mnemonics: The Sunk Cost Fallacy as a Memory
Kludge”, Northwestern University, mimeo.
[2] Bernheim, D. (2009), “On the Potential of Neuroeconomics: A Sober (but Hope-
ful) Appraisal”, American Economic Journal: Microeconomics 1 (2), 1-41.
[3] Binmore, K. and A. Shaked (2010), “Experimental Economics: Where Next?”
Journal of Economic Behavior & Organization 3 (1), 87-100.
[4] Caplin A. and A. Schotter, eds. (2008), Perspectives on the Future of Economics:
Positive and Normative Foundations, Handbook of Economic Methodology, Vol.
1, Oxford University Press.
[5] Compte, O. and A. Postelwaite (2005), “Confidence-Enhanced Performance”,
American Economic Review 94, 1536-1557.
[6] Dekel E. and B. Lipman (2009), “How (Not) to Do Decision Theory”, Annual
Review of Economics, forthcoming.
[7] Kamenica, E. (2008), “Contextual Inference in Markets: On the Informational
Content of Product Lines”, American Economic Review 98, 2127—2149.
[8] Lucas, R. (1976), “Econometric Policy Evaluation: A Critique”, in Carnegie-
Rochester conference series on public policy, Volume 1, pp. 19—46, Elsevier.
20
[9] Rabin, M. (2002), “A Perspective on Psychology and Economics”, European Eco-
nomic Review 46, 657—685.
[10] Rubinstein, A. (2006), “Dilemmas of An Economic Theorist”, Econometrica 74,
865-883.
[11] Sameulson, L. (2001), “Analogies, Adaptations, and Anomalies,” Journal of Eco-
nomic Theory 97, 320-367.
[12] Spiegler, R. (2006a), “The Market for Quacks”, Review of Economic Studies 73,
1113—1131.
[13] Spiegler, R. (2006b), “Competition Over Agents with Boundedly Rational Expec-
tations”, Theoretical Economics 1, 207—231.
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